5.3 - Factoring Trinomials Of The Form Y X 2 Bx C

KEY CONCEPTSFactoring is the opposite of expanding.To factor simple trinomials in the form x2 bx c, find two numbers suchthatWhen you multiply them, their product (P) is equal to cWhen you add them, their sum (S) is equal to b.To factor x2 bx, rewrite as x2 bx 0 or find the greatest common factor(GCF).A polynomial in the form x2 - r2 is a difference of squares. The factors are(x r)(x – r).Check the factors by expanding.

EXAMPLE 1Common FactoringTo factor polynomials by common factoring, you must first identify thegreatest common factor, or GCF. A number, variable or combination of the two, which divides evenly intoeach termSTEPSCommon factor the following expressions(a)2xGCF 2x2 – 18x2x 2x2x ((A)x –9(B))*** Check by expanding:2x(x – 9) 2x2 – 18x1. Find the GCF for bothterms. Write the GCF inthe space (A).2. Divide each term bythe GCF. Write youranswer in the space (B).This will be your finalanswer.

EXAMPLE 1Common FactoringTo factor polynomials by common factoring, you must first identify thegreatest common factor, or GCF. A number, variable or combination of the two, which divides evenly intoeach termSTEPSCommon factor the following expressions(b)8x2 24x8x 8x8x ((A)x 3 )(B)8xGCF 1. Find the GCF for bothterms. Write the GCF inthe space (A).2. Divide each term bythe GCF. Write youranswer in the space (B).This will be your finalanswer.

EXAMPLE 1Common FactoringTo factor polynomials by common factoring, you must first identify thegreatest common factor, or GCF. A number, variable or combination of the two, which divides evenly intoeach termSTEPSCommon factor the following expressions(c)16x2 – 4x 204444GCF 44x2 – x 5 ) ((A)(B)*** Check by expanding:4(4x2 – x 5) 16x2 – 4x 201. Find the GCF for bothterms. Write the GCF inthe space (A).2. Divide each term bythe GCF. Write youranswer in the space (B).This will be your finalanswer.

EXAMPLE 2Factoring Trinomials in the Form y x2 bx cFactor the following trinomials:(a)x2 15x 36 (x 3)(x 12)(b)x2 7x – 18 (x 9)(x – 2)(c)x2 – 10x 25 (x – 5)(x – 5) (x – 5)2To factor simple trinomialsin the form x2 bx c, findtwo numbers such thatP 3615S 3 12 When you multiplythem, their product (P) isequal to cP –187S 9 When you add them,their sum (S) is equal to b.P 2510S ––5–2–5

EXAMPLE 3Factoring a Difference of SquaresTo factor a difference ofsquares in the form x2 – r2Factor the following:(a)(b)(c)x2 – 16 ( x 4 )( x – 4 )x2 – 64 ( x 8 )( x – 8 )x2 – 9 ( x 3 )( x – 3 )x 2 x416 xx 2 864 x 2 x9 3 Open up two sets ofbrackets Write a “ ” in the firstbracket and “-“ in the second Take the square root of thefirst term and place thisanswer in the first space inboth brackets Take the square root of thesecond term and place thisanswer in the second space ofboth brackets. This will giveyou the final answer.

EXAMPLE 4Difference of AreasFind an expression, in factored form, for the shaded area of this figure.Recall that the area of a rectangle is Area Length WidthStep 1: Find the area of the larger shapeAlarge Length Width (x)(x) x2Step 2: Find the area of the smaller shapeAsmall Length Width (7)(7) 49

EXAMPLE 4Difference of AreasFind an expression, in factored form, for the shaded area of this figure.Step 3: Find the Area of the shaded regionShaded area Alarge – Asmall x2 – 49Step 4: Factor the expressionAlarge Length Width (x)(x) x2Asmall Length Width (7)(7) 49Shaded area x2 – 49 ( x 7 )( x – 7 )xx 2 749 This is adifference ofsquares!

Homework:Page 253 – 255#1, 2, 3acegh, 6a-c, 7ae, 8, 9, 11, *13

Microsoft PowerPoint - 5.3 - Factoring Trinomials of the Form y x 2 bx c [Compatibility Mode] Author: admin Created Date: 3/21/2020 12:49:32 PM .